All of these subtle signals (and more) are used when a dog is trying to either calm himself or you, or show the other dog that they mean no harm. They mean that the dog is anxious, either about the person or the situation they find themselves in.
A lot of these signals are used in different ways, depending on the situation.
Lip Licking - quick little flicks of the tongue or licking their nose. Sometimes the lip lick is such a tiny movement that you can barely see it. Other times it's right in your face!
Sniffing the ground - of course, dogs also sniff the ground to check their p-mail, so you must be observant. This kind of sniffing is a way of avoiding the situation, you or the approaching dog.
Play bow - front end down, back end up. This is usually an invitation to play but if they hold this position, they're saying, "I'm not a threat."
Sitting or Slowing Down
Laying Down
Tail Wagging - check the dog's body language. Dogs will also wag their tails when they're excited or aggressive. That kind of body language will be stiff. You want to see their body loose, soft, with fluid movement. If only the tip of the tail is moving, that's a sign they're unsure.
Yawning - this is a way of saying "Chill out!". It also helps them relax themselves.
Turning their head away (avoiding) - anxiety, leave me alone and let me calm down.
Turning their body away, turning to the side.
Shaking Off - exactly the same as when they shake to get rid of water on their coat. They use this as a way of calming themselves down.
Things To Be Careful Of:
Whale eye - where you can see the whites of their eyes.
Sitting down with one front paw lifted, a closed mouth or being very still - If you see a dog doing one or a combination of these things - BACK OFF. Usually this dog is one step away from biting you, whatever or whomever is making him feel nervous.
Look at the dog below. See the whale eye, the stiff body language and the closed mouth?
A lifted front paw while they're standing is usually an indication of prey drive. Prey drive would show with a very still body, a focused stare and the lifted paw.
What I find fascinating is to go to a place frequented by dogs (like the vet's office or a pet store), get down on their level and watch the dogs. There's a whole world of communication going on right under our noses!
Below are some good sites on calming signals and how to read your dog's body language.
Pit Bull Talk Forum - Calming Signals